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Simplifying Q2 + 12Q + 81 = 2Q + 12 Reorder the terms: 81 + 12Q + Q2 = 2Q + 12 Reorder the terms: 81 + 12Q + Q2 = 12 + 2Q Solving 81 + 12Q + Q2 = 12 + 2Q Solving for variable 'Q'. Reorder the terms: 81 + -12 + 12Q + -2Q + Q2 = 12 + 2Q + -12 + -2Q Combine like terms: 81 + -12 = 69 69 + 12Q + -2Q + Q2 = 12 + 2Q + -12 + -2Q Combine like terms: 12Q + -2Q = 10Q 69 + 10Q + Q2 = 12 + 2Q + -12 + -2Q Reorder the terms: 69 + 10Q + Q2 = 12 + -12 + 2Q + -2Q Combine like terms: 12 + -12 = 0 69 + 10Q + Q2 = 0 + 2Q + -2Q 69 + 10Q + Q2 = 2Q + -2Q Combine like terms: 2Q + -2Q = 0 69 + 10Q + Q2 = 0 Begin completing the square. Move the constant term to the right: Add '-69' to each side of the equation. 69 + 10Q + -69 + Q2 = 0 + -69 Reorder the terms: 69 + -69 + 10Q + Q2 = 0 + -69 Combine like terms: 69 + -69 = 0 0 + 10Q + Q2 = 0 + -69 10Q + Q2 = 0 + -69 Combine like terms: 0 + -69 = -69 10Q + Q2 = -69 The Q term is 10Q. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10Q + 25 + Q2 = -69 + 25 Reorder the terms: 25 + 10Q + Q2 = -69 + 25 Combine like terms: -69 + 25 = -44 25 + 10Q + Q2 = -44 Factor a perfect square on the left side: (Q + 5)(Q + 5) = -44 Can't calculate square root of the right side. The solution to this equation could not be determined.
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